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Is this problem correctly stated? Substituting in x=f(y) you get f(f(f(y))) = 3f(y) so f(3y) = 3f(y) This suggests a linear solution but then you get f(
by fyp 7y ago
Is this problem correctly stated? Substituting in x=f(y) you get
f(f(f(y))) = 3f(y)
so
f(3y) = 3f(y)
This suggests a linear solution but then you get f(x)=sqrt(3)x which doesn't work since it's N -> N.
- Chinjut 7y agoSuggests is not demands. If we discard the requirement to be an increasing function, one recursively defined solution takes f(3x + 1) = 3x + 2, f(3x + 2) = 3 * (3x + 1), and f(3x) = 3f(x), with f(0) = 0. Or analogously for any way of splitting the positive integers not divisible by 3 into ordered pairs (a, b). Then define f(3^n a) = 3^n b and f(3^n b) = 3^(n + 1) a. This is the general form of the solutions.